Quantifying Multimodal Capabilities: Formal Generalization Guarantees in Pairwise Metric Learning

2026-05-02

AI Summary

This work addresses the practical challenges in multimodal learning caused by missing or redundant modalities and the lack of theoretical understanding of how modality selection affects performance. It presents the first joint analysis of how the number of modalities and feature granularity influence generalization. By constructing a hierarchical structure of function classes corresponding to different modality subsets and leveraging pairwise complexity measures, the study derives generalization error bounds that quantify the discrepancy between the learned mapping and the true underlying mapping. The theoretical results demonstrate that fine-grained modality features effectively reduce hypothesis space complexity and enhance modality complementarity, thereby improving both convergence rates and prediction accuracy. These findings provide a rigorous theoretical foundation for designing effective multimodal learning systems.

Abstract

Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a fine-grained theoretical analysis of the generalization properties of multimodal metric learning models, addressing critical gaps in understanding the relationship between modality selection and algorithmic performance. We establish hierarchical relationships between function classes corresponding to different modality subsets and quantify the discrepancy between learned mappings and ground truth. Through rigorous analysis of pairwise complexity within the multimodal learning framework, we derive novel generalization error bounds that reveal the joint impact of modality quantity and granularity on model performance. Our theoretical findings on both upper and lower bounds demonstrate that incorporating fine-grained modality features reduces the complexity of the hypothesis space by enhancing modality complementarity. This work offers both theoretical foundations and practical implications for improving convergence rates and accuracy in multimodal learning systems.

Problem

• multimodal learning
• generalization guarantees
• metric learning
• modality selection
• pairwise complexity

Innovation

• multimodal learning
• metric learning
• generalization bounds
• modality complementarity
• pairwise complexity